Pub Date : 2025-06-25DOI: 10.1109/JSAIT.2025.3583217
Jessalyn Bolkema;Emma Andrade;Thomas Dexter;Harrison Eggers;Victoria L. Fisher;Luke Szramowsky;Felice Manganiello
CSS-T codes are a class of stabilizer codes introduced by Rengaswamy et al. with desired properties for quantum fault-tolerance. In this work, we comprehensively study non-degenerate CSS-T codes built from Reed-Muller codes. These classical codes allow for constructing optimal CSS-T code families with nonvanishing asymptotic rates up to ${}frac {1}{2}$ and possibly diverging minimum distance when non-degenerate.
{"title":"CSS-T Codes From Reed-Muller Codes","authors":"Jessalyn Bolkema;Emma Andrade;Thomas Dexter;Harrison Eggers;Victoria L. Fisher;Luke Szramowsky;Felice Manganiello","doi":"10.1109/JSAIT.2025.3583217","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3583217","url":null,"abstract":"CSS-T codes are a class of stabilizer codes introduced by Rengaswamy et al. with desired properties for quantum fault-tolerance. In this work, we comprehensively study non-degenerate CSS-T codes built from Reed-Muller codes. These classical codes allow for constructing optimal CSS-T code families with nonvanishing asymptotic rates up to <inline-formula> <tex-math>${}frac {1}{2}$ </tex-math></inline-formula> and possibly diverging minimum distance when non-degenerate.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"199-204"},"PeriodicalIF":0.0,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144634775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-23DOI: 10.1109/JSAIT.2025.3582156
Elena Berardini;Reza Dastbasteh;Josu Etxezarreta Martinez;Shreyas Jain;Olatz Sanz Larrarte
We propose a new systematic construction of CSS-T codes from any given CSS code using a map $phi $ . When $phi $ is the identity map I, we retrieve the construction of Hu et al. (2021) and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction $(phi = I)$ , concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in Jain and Albert (2024). Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation.
{"title":"Asymptotically Good CSS-T Codes and a New Construction of Triorthogonal Codes","authors":"Elena Berardini;Reza Dastbasteh;Josu Etxezarreta Martinez;Shreyas Jain;Olatz Sanz Larrarte","doi":"10.1109/JSAIT.2025.3582156","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3582156","url":null,"abstract":"We propose a new systematic construction of CSS-T codes from any given CSS code using a map <inline-formula> <tex-math>$phi $ </tex-math></inline-formula>. When <inline-formula> <tex-math>$phi $ </tex-math></inline-formula> is the identity map I, we retrieve the construction of Hu et al. (2021) and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction <inline-formula> <tex-math>$(phi = I)$ </tex-math></inline-formula>, concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in Jain and Albert (2024). Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"189-198"},"PeriodicalIF":0.0,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144634708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-20DOI: 10.1109/JSAIT.2025.3581810
Tzu-Hao Lin;Ching-Yi Lai
In this paper, we introduce the Union-Intersection Union-Find (UIUF) algorithm for decoding depolarizing errors in topological codes, combining the strengths of iterative and standard Union-Find (UF) decoding. While iterative UF improves performance at moderate error rates, it lacks an error correction guarantee. To address this, we develop UIUF, which maintains the enhanced performance of iterative UF while ensuring error correction up to half the code distance. Through simulations under code capacity, phenomenological, and biased noise models, we show that UIUF significantly outperforms UF, reducing the logical error rate by over an order of magnitude (at around $10^{-5}$ ). Moreover, UIUF achieves lower logical error rates than the Minimum Weight Perfect Matching (MWPM) decoder on rotated surface codes under both the code capacity and phenomenological noise models, while preserving efficient linear-time complexity.
{"title":"Union-Intersection Union-Find for Decoding Depolarizing Errors in Topological Codes","authors":"Tzu-Hao Lin;Ching-Yi Lai","doi":"10.1109/JSAIT.2025.3581810","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3581810","url":null,"abstract":"In this paper, we introduce the Union-Intersection Union-Find (UIUF) algorithm for decoding depolarizing errors in topological codes, combining the strengths of iterative and standard Union-Find (UF) decoding. While iterative UF improves performance at moderate error rates, it lacks an error correction guarantee. To address this, we develop UIUF, which maintains the enhanced performance of iterative UF while ensuring error correction up to half the code distance. Through simulations under code capacity, phenomenological, and biased noise models, we show that UIUF significantly outperforms UF, reducing the logical error rate by over an order of magnitude (at around <inline-formula> <tex-math>$10^{-5}$ </tex-math></inline-formula>). Moreover, UIUF achieves lower logical error rates than the Minimum Weight Perfect Matching (MWPM) decoder on rotated surface codes under both the code capacity and phenomenological noise models, while preserving efficient linear-time complexity.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"163-175"},"PeriodicalIF":0.0,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144606250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-11DOI: 10.1109/JSAIT.2025.3578597
Hanwen Yao;Mert Gökduman;Henry D. Pfister
We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connolly et al. in 2022. Like the VH decoder, the idea is to first run the peeling decoder and then post-process the resulting stopping set. The cluster decoder breaks the stopping set into a tree of clusters, which can be solved sequentially via Gaussian Elimination. By allowing clusters of unconstrained size, this decoder achieves maximum-likelihood (ML) performance with reduced complexity compared with full Gaussian Elimination. When Gaussian Elimination is applied only to clusters whose sizes are less than a constant, the performance is degraded, but the complexity becomes linear in the block length. Our simulation results show that, for hypergraph product codes, the cluster decoder with constant cluster size achieves near-ML performance similar to VH decoding in the low-erasure-rate regime. For the general quantum LDPC codes we studied, the cluster decoder can be used to estimate the ML performance curve with reduced complexity over a wide range of erasure rates.
{"title":"Cluster Decomposition for Improved Erasure Decoding of Quantum LDPC Codes","authors":"Hanwen Yao;Mert Gökduman;Henry D. Pfister","doi":"10.1109/JSAIT.2025.3578597","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3578597","url":null,"abstract":"We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connolly et al. in 2022. Like the VH decoder, the idea is to first run the peeling decoder and then post-process the resulting stopping set. The cluster decoder breaks the stopping set into a tree of clusters, which can be solved sequentially via Gaussian Elimination. By allowing clusters of unconstrained size, this decoder achieves maximum-likelihood (ML) performance with reduced complexity compared with full Gaussian Elimination. When Gaussian Elimination is applied only to clusters whose sizes are less than a constant, the performance is degraded, but the complexity becomes linear in the block length. Our simulation results show that, for hypergraph product codes, the cluster decoder with constant cluster size achieves near-ML performance similar to VH decoding in the low-erasure-rate regime. For the general quantum LDPC codes we studied, the cluster decoder can be used to estimate the ML performance curve with reduced complexity over a wide range of erasure rates.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"176-188"},"PeriodicalIF":0.0,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144606314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. Both of these techniques have been generalized to quantum codes. Restricting to stabilizer codes, this paper introduces more freedom in the choice of the encoded states after puncturing. Furthermore, we also give an explicit description of the stabilizers for the punctured code. The additional freedom in the procedure also opens up for new ways to construct new codes from old, and we present several ways to utilize this in the search for codes with good or even optimal parameters. In particular, we use the construction to obtain codes whose parameters exceed the best previously known and which are better than what general puncturing guarantees. Lastly, the freedom in our puncture procedure allowed us to generalize the proof of the Griesmer bound from the classical setting to stabilizer codes for qudits of prime dimension since the proof relies heavily on the puncturing technique.
{"title":"Puncturing Quantum Stabilizer Codes","authors":"Jaron Skovsted Gundersen;René Bødker Christensen;Markus Grassl;Petar Popovski;Rafał Wisniewski","doi":"10.1109/JSAIT.2025.3562287","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3562287","url":null,"abstract":"Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. Both of these techniques have been generalized to quantum codes. Restricting to stabilizer codes, this paper introduces more freedom in the choice of the encoded states after puncturing. Furthermore, we also give an explicit description of the stabilizers for the punctured code. The additional freedom in the procedure also opens up for new ways to construct new codes from old, and we present several ways to utilize this in the search for codes with good or even optimal parameters. In particular, we use the construction to obtain codes whose parameters exceed the best previously known and which are better than what general puncturing guarantees. Lastly, the freedom in our puncture procedure allowed us to generalize the proof of the Griesmer bound from the classical setting to stabilizer codes for qudits of prime dimension since the proof relies heavily on the puncturing technique.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"74-84"},"PeriodicalIF":0.0,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-30DOI: 10.1109/JSAIT.2025.3575095
Yongxi Liu;Ming Zhang;Xiaoming Chen;Anxue Zhang
Antenna efficiency is a key parameter in the design of large-scale dense arrays, and influences the signal-to-noise ratio (SNR) of wireless communications. Low embedded element efficiency (EEE) has been verified to be the bottleneck of dense array MIMO systems. Using ideas from the Floquet series, we propose a new framework to evaluate the mutual coupling for infinite arrays with a regular grid, including two new methods to calculate the EEE. The proposed methods can incorporate the impedance of the source network, whereas the traditional geometry based method assumes perfect impedance matching at all scan angles. Starting from the surface current of array elements, the radiation field is decomposed into a set of current-weighted orthogonal electromagnetic waves. This decomposition can be utilized to compute the radiation characteristics of the antenna array, including the active impedance, the generalized scattering parameters, and the embedded element patterns. Theoretical analysis is provided to illustrate how the degradation of EEE reduces the SNR and sequentially channel capacity of MIMO systems. Numerical simulations show that the proposed methods give a more accurate efficiency than the geometry based method. Channel capacity based on the polarization holographic channel model is evaluated to validate the constraining effect of EEE on system throughput.
{"title":"A Floquet Series-Based Framework to Evaluate the Impact of Antenna Efficiency on MIMO Systems","authors":"Yongxi Liu;Ming Zhang;Xiaoming Chen;Anxue Zhang","doi":"10.1109/JSAIT.2025.3575095","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3575095","url":null,"abstract":"Antenna efficiency is a key parameter in the design of large-scale dense arrays, and influences the signal-to-noise ratio (SNR) of wireless communications. Low embedded element efficiency (EEE) has been verified to be the bottleneck of dense array MIMO systems. Using ideas from the Floquet series, we propose a new framework to evaluate the mutual coupling for infinite arrays with a regular grid, including two new methods to calculate the EEE. The proposed methods can incorporate the impedance of the source network, whereas the traditional geometry based method assumes perfect impedance matching at all scan angles. Starting from the surface current of array elements, the radiation field is decomposed into a set of current-weighted orthogonal electromagnetic waves. This decomposition can be utilized to compute the radiation characteristics of the antenna array, including the active impedance, the generalized scattering parameters, and the embedded element patterns. Theoretical analysis is provided to illustrate how the degradation of EEE reduces the SNR and sequentially channel capacity of MIMO systems. Numerical simulations show that the proposed methods give a more accurate efficiency than the geometry based method. Channel capacity based on the polarization holographic channel model is evaluated to validate the constraining effect of EEE on system throughput.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"150-162"},"PeriodicalIF":0.0,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144481946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-26DOI: 10.1109/JSAIT.2025.3555066
Thomas L. Marzetta;Brian McMinn;Amritpal Singh;Thorkild B. Hansen
Subject to the laws of classical physics - the science that governs the design of today’s wireless communication systems - there is no need to match the radiation impedance of a receiver antenna to the impedance of the front-end electronics in order to effect communications. If we dispense with a transmission line and, instead, make the front-end electronics colocated with the antenna, then a high input impedance preamplifier can measure the open-circuit voltage directly on the antenna port while drawing negligible power. Neither Friis’ concept of noise figure, nor Shannon information theory, nor electronics technology dictates that we must extract power from an antenna. Classical physics appears not to provide a lower bound on the energy that must be extracted from the antenna for every bit of received information.
{"title":"How Much Power Must We Extract From a Receiver Antenna to Effect Communications?","authors":"Thomas L. Marzetta;Brian McMinn;Amritpal Singh;Thorkild B. Hansen","doi":"10.1109/JSAIT.2025.3555066","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3555066","url":null,"abstract":"Subject to the laws of classical physics - the science that governs the design of today’s wireless communication systems - there is no need to match the radiation impedance of a receiver antenna to the impedance of the front-end electronics in order to effect communications. If we dispense with a transmission line and, instead, make the front-end electronics colocated with the antenna, then a high input impedance preamplifier can measure the open-circuit voltage directly on the antenna port while drawing negligible power. Neither Friis’ concept of noise figure, nor Shannon information theory, nor electronics technology dictates that we must extract power from an antenna. Classical physics appears not to provide a lower bound on the energy that must be extracted from the antenna for every bit of received information.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"49-58"},"PeriodicalIF":0.0,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143800996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-25DOI: 10.1109/JSAIT.2025.3554625
Yuxiang Lu;Syed A. Jafar
A communication-efficient protocol is introduced over a many-to-one quantum network for Q-E-B-MDS-X-TPIR, i.e., quantum private information retrieval with MDS-X-secure storage and T-private queries. The protocol is resilient to any set of up to E unresponsive servers (erased servers or stragglers) and any set of up to B Byzantine servers. The underlying coding scheme incorporates an enhanced version of a Cross Subspace Alignment (CSA) code, namely a Modified CSA (MCSA) code, into the framework of CSS codes. The error-correcting capabilities of CSS codes are leveraged to encode the dimensions that carry desired computation results from the MCSA code into the error space of the CSS code, while the undesired interference terms are aligned into the stabilized code space. The challenge is to do this efficiently while also correcting quantum erasures and Byzantine errors. The protocol achieves superdense coding gain over comparable classical baselines for Q-E-B-MDS-X-TPIR, recovers as special cases the state of art results for various other quantum PIR settings previously studied in the literature, and paves the way for applications in quantum coded distributed computation, where CSA code structures are important for communication efficiency, while security and resilience to stragglers and Byzantine servers are critical.
{"title":"Quantum X-Secure T-Private Information Retrieval From MDS Coded Storage With Unresponsive and Byzantine Servers","authors":"Yuxiang Lu;Syed A. Jafar","doi":"10.1109/JSAIT.2025.3554625","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3554625","url":null,"abstract":"A communication-efficient protocol is introduced over a many-to-one quantum network for Q-E-B-MDS-X-TPIR, i.e., quantum private information retrieval with MDS-<italic>X</i>-secure storage and <italic>T</i>-private queries. The protocol is resilient to any set of up to <italic>E</i> unresponsive servers (erased servers or stragglers) and any set of up to <italic>B</i> Byzantine servers. The underlying coding scheme incorporates an enhanced version of a Cross Subspace Alignment (CSA) code, namely a Modified CSA (MCSA) code, into the framework of CSS codes. The error-correcting capabilities of CSS codes are leveraged to encode the dimensions that carry desired computation results from the MCSA code into the error space of the CSS code, while the undesired interference terms are aligned into the stabilized code space. The challenge is to do this efficiently while also correcting quantum erasures and Byzantine errors. The protocol achieves superdense coding gain over comparable classical baselines for Q-E-B-MDS-X-TPIR, recovers as special cases the state of art results for various other quantum PIR settings previously studied in the literature, and paves the way for applications in quantum coded distributed computation, where CSA code structures are important for communication efficiency, while security and resilience to stragglers and Byzantine servers are critical.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"59-73"},"PeriodicalIF":0.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143800744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-21DOI: 10.1109/JSAIT.2025.3553733
Divyakumar Badheka;Jacob J. Adams;Brian L. Hughes
In MIMO communications, information about the transmitted signal is conveyed to the receiver through fields and currents on the surface of the receive antenna array. However, this information can only be observed indirectly through the ports of the array. This raises fundamental information-theoretic questions: How much useful information is contained in the fields and currents on the surface of the receiver array? How much of this information is captured by the array ports? Do conventional arrays efficiently extract the information contained in their conducting surfaces? In this paper, we consider these questions in the context of a multiuser MIMO (MU-MIMO) uplink where users are separated by spatial beamforming at the receiver. Our main results can be summarized as follows: To quantify the information contained in the EM fields and currents on the surface of the receiving antenna array, we first introduce a new model, the surface receiver model. We then use this model to derive upper bounds on the spectral efficiency that can be approached with any location of M ports on the surface of the receiving antenna array. We denote this the surface modal bound. Furthermore, we also derive upper bound on the spectral efficiency approached with any number or location of ports on the receiver array. We call it the surface spectral efficiency. Finally, we apply the analytical results to a MU-MIMO uplink with an array of patch antennas at the receiver. The results suggests that the conventional arrays of single and dual-polarized patches fails to capture most of the information contained in the surface currents. The results further suggest ways to modify the number of antenna ports, together with the receiver front-end, to extract the information in the surface currents more efficiently.
{"title":"Limits in Spectral Efficiency From Array Geometry","authors":"Divyakumar Badheka;Jacob J. Adams;Brian L. Hughes","doi":"10.1109/JSAIT.2025.3553733","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3553733","url":null,"abstract":"In MIMO communications, information about the transmitted signal is conveyed to the receiver through fields and currents on the surface of the receive antenna array. However, this information can only be observed indirectly through the ports of the array. This raises fundamental information-theoretic questions: How much useful information is contained in the fields and currents on the surface of the receiver array? How much of this information is captured by the array ports? Do conventional arrays efficiently extract the information contained in their conducting surfaces? In this paper, we consider these questions in the context of a multiuser MIMO (MU-MIMO) uplink where users are separated by spatial beamforming at the receiver. Our main results can be summarized as follows: To quantify the information contained in the EM fields and currents on the surface of the receiving antenna array, we first introduce a new model, the surface receiver model. We then use this model to derive upper bounds on the spectral efficiency that can be approached with any location of M ports on the surface of the receiving antenna array. We denote this the surface modal bound. Furthermore, we also derive upper bound on the spectral efficiency approached with any number or location of ports on the receiver array. We call it the surface spectral efficiency. Finally, we apply the analytical results to a MU-MIMO uplink with an array of patch antennas at the receiver. The results suggests that the conventional arrays of single and dual-polarized patches fails to capture most of the information contained in the surface currents. The results further suggest ways to modify the number of antenna ports, together with the receiver front-end, to extract the information in the surface currents more efficiently.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"34-48"},"PeriodicalIF":0.0,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10937211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-19DOI: 10.1109/JSAIT.2025.3571313
Julien Du Crest;Mehdi Mhalla;Valentin Savin
Kitaev’s toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes. Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs. Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process. We show that if the unsatisfied checks of an error syndrome are at distance $ge 5$ from each other, then MS decoding is locally blind: the qubits in the direct neighborhood of an unsatisfied check are never aware of any other unsatisfied checks, except their direct neighbor. Moreover, we show that degeneracy is not the only cause of decoding failures for errors of weight at least 4, that is, the MS non-degenerate decoding radius is equal to 3, for any toric code of distance $ge 9$ . Finally, complementing our theoretical analysis, we present a pre-processing method of practical relevance. The proposed method, referred to as stabiliser blowup, has linear complexity and allows correcting all (degenerate) errors of weight up to 3, providing quadratic improvement in the logical error rate performance, as compared to MS alone.
{"title":"A Blindness Property of the Min-Sum Decoding for the Toric Code","authors":"Julien Du Crest;Mehdi Mhalla;Valentin Savin","doi":"10.1109/JSAIT.2025.3571313","DOIUrl":"https://doi.org/10.1109/JSAIT.2025.3571313","url":null,"abstract":"Kitaev’s toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes. Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs. Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process. We show that if the unsatisfied checks of an error syndrome are at distance <inline-formula> <tex-math>$ge 5$ </tex-math></inline-formula> from each other, then MS decoding is locally blind: the qubits in the direct neighborhood of an unsatisfied check are never aware of any other unsatisfied checks, except their direct neighbor. Moreover, we show that degeneracy is not the only cause of decoding failures for errors of weight at least 4, that is, the MS non-degenerate decoding radius is equal to 3, for any toric code of distance <inline-formula> <tex-math>$ge 9$ </tex-math></inline-formula>. Finally, complementing our theoretical analysis, we present a pre-processing method of practical relevance. The proposed method, referred to as stabiliser blowup, has linear complexity and allows correcting all (degenerate) errors of weight up to 3, providing quadratic improvement in the logical error rate performance, as compared to MS alone.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"6 ","pages":"138-149"},"PeriodicalIF":2.2,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：